<TeXmacs|2.1>

<style|<tuple|tmdoc|maxima|english|old-spacing|old-dots|old-lengths>>

<\body>
  <\tmdoc-title>
    Example <name|Eukleides> session
  </tmdoc-title>

  Here follows a sample session, which was started using
  <menu|Insert|Session|Eukleides>.

  <\session|eukleides|default>
    <\output>
      <math|E*\<Upsilon\>*K*\<Lambda\>*EI \<Delta\>*H*\<Sigma\>>

      A Euclidean Geometry Drawing Language

      Eukleides version 1.5.4

      Copyright (c) Christian Obrecht 2004-2010
    </output>

    <\unfolded-subsession>
      <strong|Tangents to a circle>
    <|unfolded-subsession>
      <\unfolded-io>
        eukleides]\ 
      <|unfolded-io>
        O = point(2, 2)

        C = circle(O, 2)

        A = point(6.5, 2)

        \;

        c = circle(O.A)

        I.J = intersection(C, c)

        \;

        draw

        \ \ line(A, I) gray

        \ \ line(A, J) gray

        \ \ C ; c dashed, gray

        \ \ O plus ; A

        end
      <|unfolded-io>
        <image|<tuple|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|ps>|0.618par|||>
      </unfolded-io>

      <\input>
        Eukleides]\ 
      <|input>
        \;
      </input>
    </unfolded-subsession>

    <\unfolded-subsession>
      <strong|Feuerbach's circle>
    <|unfolded-subsession>
      <\unfolded-io>
        eukleides]\ 
      <|unfolded-io>
        A B C triangle

        \;

        A' = projection(A, line(B, C))

        B' = projection(B, line(C, A))

        C' = projection(C, line(A, B))

        \;

        A_0 = midpoint(B.C)

        B_0 = midpoint(C.A)

        C_0 = midpoint(A.B)

        \;

        draw

        \ \ (A.B.C)

        \ \ circle(A', B', C')

        \ \ A'; B'; C'

        \ \ A_0 ; B_0 ; C_0

        end

        draw dashed

        \ \ A.A' ; B.B' ; C.C'

        end

        \;

        label

        \ \ A -135: ; B -45: ; C 90:

        \ \ A' 45: ; B' 135: ; C' -90:

        \ \ A_0 30: ; B_0 150: ; C_0 -90:

        end
      <|unfolded-io>
        <image|<tuple|<#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>|ps>|0.618par|||>
      </unfolded-io>

      <\input>
        Eukleides]\ 
      <|input>
        \;
      </input>
    </unfolded-subsession>

    <\unfolded-subsession>
      <strong|Pascal's theorem>
    <|unfolded-subsession>
      <\unfolded-io>
        eukleides]\ 
      <|unfolded-io>
        box -3, -4, 7, 8

        \;

        e = ellipse(point(0,0), 2, 1, 0 rad)

        \;

        A = point(e, 0 rad)

        B = point(e, pi/5 rad)

        C = point(e, 2*pi/3 rad)

        D = point(e, pi rad)

        E = point(e, 3*pi/2 rad)

        F = point(e, 11*pi/6 rad)

        \;

        AB = line(A, B)

        BC = line(B, C)

        CD = line(C, D)

        DE = line(D, E)

        EF = line(E, F)

        FA = line(F, A)

        \;

        I = intersection(AB,DE)

        J = intersection(FA,CD)

        \;

        draw dashed, gray

        \ \ AB ; BC ; CD ; DE ; EF ; FA

        end

        \;

        draw

        \ \ line(I, J)

        \ \ (A.B.C.D.E.F) gray

        \ \ e

        end
      <|unfolded-io>
        <image|<tuple|<#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>|ps>|0.618par|||>
      </unfolded-io>

      <\input>
        Eukleides]\ 
      <|input>
        \;
      </input>
    </unfolded-subsession>
  </session>

  <tmdoc-copyright|2012-2021|Joris van der Hoeven>

  <tmdoc-license|Permission is granted to copy, distribute and/or modify this
  document under the terms of the GNU Free Documentation License, Version 1.1
  or any later version published by the Free Software Foundation; with no
  Invariant Sections, with no Front-Cover Texts, and with no Back-Cover
  Texts. A copy of the license is included in the section entitled "GNU Free
  Documentation License".>
</body>

<initial|<\collection>
</collection>>